In a large shallow bowl, mix together the olive oil, balsamic vinegar, garlic, oregano, basil, salt and pepper. Add in the chicken and allow to marinate for half an hour (if time allows).
Preheat grill plates over medium heat, and grill chicken for 5-6 minutes each side, or until completely cooked through in the centre, and slightly charred on the outer edges. While chicken is cooking, grill the tomato slices for 1-2 minutes each side. Top each breast with a slice of mozzarella and grilled tomato slice, allowing the heat to melt the cheese.
To serve, top with the shredded basil and balsamic reduction.